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OPERATIONAL DEFINITION: DIMENSIONS AND ELEMENTS 183

Figure 8.2
Dimensions (D) and elements (E) of the concept (C) learning.
C
Learning

D D D

Understanding Retention (recall) Application

E E E E E
Solve problems Integrate
Answer questions Give appropriate Recall material applying concepts with other
correctly examples after some lapse understood and relevant
of time recalled material

can measure the concept of learning. A schematic diagram of the operational
definition of the concept of learning is shown in Figure 8.2. The diagram will
facilitate our understanding of the discussion that follows.
A teacher can assess whether students have understood a concept that has
been just taught by asking them to explain it and furnishing suitable exam-
ples. If they answer correctly, the teacher may assume that the students have
understood. By giving a test a week or month later, the teacher can measure
for how long they remember what has been taught. By asking them to apply
the concepts learned in a new problem situation, the teacher can also mea-
sure how much they can put into application what is understood. If they solve
the problem successfully using the material taught to them in class, the teacher
will be reasonably assured that learning has indeed been achieved. To the
extent that they do not successfully apply the concepts taught, learning might
not have advanced to the degree expected. Note that in this case, application
of the relevant concepts subsumes both understanding and retention. That
is, one cannot apply the concepts unless one has understood them and
retained them in memory. In most multiple-choice questions, understanding
and retention are generally tested; the application aspects are often not.
Exams, when properly designed, could be an effective instrument for assess-
ing the learning that students acquire during the semester. In other words, it
is possible to reliably measure learning when exam questions are well
designed to tap the students’ understanding, retention, and ability to apply
what has been taught.
Again, it is very important to remember that learning is no measure of the
effort the teacher expends in explaining, nor that put in by the student to under-
stand, though both of these naturally tend to enhance understanding. Although
both may be correlated to learning they do not actually measure it.